| $M \rightarrow \sim (S \ \&\ T)$ |
| $\sim (A \ \&\ B)\ v\ \sim D$ |
| $\sim D (S \ \&\ T)$ |
| $M$ |
| $[\sim (A \ \&\ B) \ \&\ M)\ v\ D$ |
| $(1)\ M\rightarrow \sim (S \ \&\ T)$ | $P$ |
| $(2)\ \sim (A \ \&\ B)\ v\sim D$ | $P$ |
| $(3)\ \sim D \rightarrow (S \ \&\ T)$ | $P$ |
| $(4)\ M$ | $P/[\sim (A \ \&\ B)\ \ \&\ M]\ v\ D$ |
| $(5)\ \sim (S \ \&\ T)$ | $1, 4, MP$ |
| $(6)\ \sim\ \sim D$ | $3, 5, MT$ |
| $(7)\ \sim (A \ \&\ B)$ | $2, 6, DS$ |
| $(8)\ \sim (A \ \&\ B)\ \ \&\ M$ | $7, 4,$ Conj. |
| $(9)\ [\sim (A \ \&\ B)\ \ \&\ M]\ v\ D$ | $8,$ Add. |
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $(T\ \&\ P) \rightarrow \sim Q$ |
| $\sim (T\ \&\ P) \rightarrow (R \rightarrow \sim Q)$ |
| $(\sim S\ v\ R)\rightarrow\ \sim\ \sim Q$ |
| $\sim S$ |
| $\therefore \sim R\ \&\ \sim S$ |
| $(A\ v\ B)\ v\ \sim\ C$ |
| $D\ \rightarrow\ [(A\ v\ B) \rightarrow\ E]$ |
| $F\ \rightarrow (\sim\ C\ \rightarrow\ G)$ |
| $D\ \&\ F$ |
| $(E\ v\ G)\ v\ H$ |